The House could vote as early as Wednesday on legislation to raise the country’s borrowing limit, after Republicans met on Monday night in their latest effort to find elusive consensus on one of the final must-pass objectives before Washington goes into election mode.

During a meeting in the basement of the Capitol, GOP leaders floated the idea of repealing a cut to veterans’ pensions set to take place next year and attach that to a bill that would raise the debt ceiling for one year. It remains to be seen if a majority of the restive conservative conference will back party leadership, or if House Speaker John Boehner will be left to rely on Democrats to take action before what the Obama Administration has pegged as a critical Feb. 27 deadline. Representative Kevin Brady, a Republican from Texas, told TIME that the measure would be paid for by extending a 2% cut in payments to Medicare providers for one more year, until 2024.

But the initial response among members was lukewarm. “I’m giving it some thought,” Brady says. “We have to pay our bills on time and in full [but] I’m worried that we’re not solving the military retirement problem for the long term.” Several members remained unsure how the increase in pension spending would be offset.

Democrats have repeatedly said they could only support a “clean” debt-limit increase, without strings attached. Financial markets, accustomed to congressional brinkmanship over the debt ceiling, have stayed calm, even though Congress blew past its self-imposed Friday deadline for resolving the issue. The Treasury Department will continue to use “extraordinary measures” to pay the country’s bills through Feb. 27. “At that point, Treasury would be left with only the cash on hand and any incoming revenue to meet our country’s commitments,” Treasury Secretary Jack Lew wrote to Boehner last week.

The Senate on Monday unanimously cleared a procedural hurdle for a bill that would repeal the veterans’ pension cut without offsetting the increase in spending. Several vulnerable Democrats up for re-election supported the measure, signaling a willingness in the upper chamber for repeal — if not necessarily as a condition of raising the debt limit.

After years of fierce partisan fiscal battles that have led the country to the brink of default, Congress’s debt-ceiling fight has this year become almost entirely a fight within the Republican Party. House GOP leadership has bounced around ideas that could be attached to an increase to garner conservatives’ support — from repealing an obscure health-care-law provision or approving the Keystone XL pipeline, to tweaking the Medicare reimbursement structure and now repealing the veterans’ pension cut — but so far to no avail. While the latest proposal may yet gain momentum, it’s low-hanging fruit that puts members in the unenviable position of being forced to vote for an increase or against higher military pensions, and a far cry from more recent conservative goals like defending the health-care-reform law. After months of Republican wrangling, Democrats united behind a no-strings-attached approach to raising the debt ceiling increasingly appear to have the upper hand. Boehner has made clear he won’t allow a debt default.